We know that trigonometric ratios can be expressed in terms of π. Let us now find the value of cos2π.
Solution
π is denoted for 180°, which is half of the rotation of a unit circle.
Hence, 2π denotes full rotation.
So, for any number of a full rotation, n, the value of cos will remain equal to 1
we know that, cos 0° = 1
Now, once we take a complete rotation in a unit circle, we reach back to the starting point.
After completing one rotation, the value of the angle is 360° or 2π in radians.
Thus, we can say, after reaching the same position,
Cos 0° = cos 360°
Or
Cos 0° = 2π
Therefore, we conclude that,
Cos 360° = cos 2π = 1
Answer
cos 2π = 1
